Defect reduction using aspect ratio trapping

ABSTRACT

Lattice-mismatched epitaxial films formed proximate non-crystalline sidewalls. Embodiments of the invention include formation of facets that direct dislocations in the films to the sidewalls.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 13/446,612, filed on Apr. 13, 2012, entitled “Defect Reduction Using Aspect Ratio Trapping,” which is a divisional of U.S. patent application Ser. No. 11/852,078, filed on Sep. 7, 2007, entitled “Defect Reduction Using Aspect Ratio Trapping,” which claims the benefit of and priority to U.S. Provisional Application Ser. No. 60/842,771, filed Sep. 7, 2006, and U.S. Provisional Application Ser. No. 60/873,903, filed Dec. 8, 2006; the entire disclosures of these applications are hereby incorporated by reference in their entireties.

FIELD OF THE INVENTION

The invention relates generally to semiconductor processing and particularly to blocking defects by aspect ratio trapping (“ART”).

BACKGROUND

The formation of lattice-mismatched materials has many practical applications. For example, germanium (Ge) heteroepitaxy on silicon (Si) is promising both for, e.g., high-performance Ge p-channel metal-oxide-semiconductor field-effect transistors (MOSFETs) and as a potential path for integrating optoelectronic devices with Si complementary metal-oxide semiconductor (CMOS) technology. Heteroepitaxially growing Ge on Si also is a path for providing a substitute for Ge wafers for many other applications such as photovoltaics and light-emitting diodes, provided that a sufficiently high-quality Ge surface can be obtained cost-effectively. Unfortunately, growing more than a few nanometers (nm) of Ge directly on Si can lead to a dislocation density of 10⁸-10⁹/cm² due to the 4.2% lattice mismatch, which is unacceptable for most applications. Various solutions involving thick epitaxial layers (most successfully to date via graded-buffer technology) or post-growth high-temperature annealing have been explored to alleviate this problem. However, for true ease of integration with Si CMOS technology, a defect reduction solution involving low epitaxial layer thickness (to meet planarity requirements for Si processing) and low thermal budget (to allow addition of Ge at any point in the process without degrading the CMOS transistor elements) is highly desirable.

SUMMARY

The “epitaxial necking” technique is effective for growing Ge on Si for small areas, e.g., circular regions of diameter ≦200 nm. Epitaxial necking involves selective growth in patterned openings bounded by substantially vertical dielectric sidewalls, enabling dislocations to be trapped under certain conditions. See E. A. Fitzgerald and N. Chand, J. Electron. Mat. 20, 839 (1991), and T. A. Langdo, C. W. Leitz, M. T. Currie, and E. A. Fitzgerald, A. Lochtefeld and D. A. Antoniadis, Appl. Phys. Lett. 76 (25), 3700 (2000). Langdo et al. demonstrated defect-free Ge regions grown by ultrahigh vacuum chemical vapor deposition in 100 nm diameter holes in SiO₂ on a Si substrate; similar results were obtained for Ge/Si grown by molecular beam epitaxy. See Qiming Li, Sang M. Han, Steven R. J. Brueck, Stephen Hersee, Ying-Bing Jiang, and Huifang Xu, Appl. Phys. Lett. 83 (24) 5032 (2003).

The present inventors have found that the orientation of the epitaxial layer surface during growth plays a dominant role in determining the configurations of many of the threading dislocations in the layers. These dislocations behave as “growth dislocations,” which, during growth, are oriented approximately normal to the growth surface that they intersect. If the normal is not parallel to a dielectric sidewall that bounds the growth opening, then the dislocations are guided out from the central regions of the patterned opening. Thus, by properly engineering the profile of the growth surface during growth, certain kinds of threading dislocations may be caused to grow out of the epitaxial layer and terminate at the dielectric sidewalls, thereby increasing the effectiveness of defect trapping.

As used herein, “aspect ratio trapping” refers generally to the technique(s) of causing defects to terminate at non-crystalline, e.g., dielectric sidewalls, where the sidewalls are sufficiently high relative to the size of the growth area so as to trap most, if not all, of the defects.

Processing conditions may be tailored to enable effective trapping of threading dislocations in trenches of arbitrary length, including, e.g., for Ge grown directly on Si via reduced pressure chemical vapor deposition (RPCVD), e.g., the deposition of Ge layers as thin as 450 nm in SiO₂ trenches having an aspect ratio >1 (“AR,” defined for trenches as the ratio of the trench height/width).

In an aspect, the invention features a method for forming a structure, the method including the steps of providing a crystalline semiconductor substrate comprising a first semiconductor material and having a top surface, and defining an opening having a non-crystalline sidewall proximate the top surface of the crystalline semiconductor substrate. An epitaxial film is formed in the opening. The epitaxial film includes a second semiconductor material that is lattice mismatched to the first semiconductor material. The epitaxial film has a growth front, the growth front including a surface having a facet substantially non-parallel to the substrate top surface. Forming the epitaxial film includes configuring epitaxial film formation parameters to cause formation of the facet. A dislocation in the epitaxial film is approximately normal to the epitaxial film surface.

In another aspect, the invention features a method for forming a structure, the method including the steps of providing a crystalline semiconductor substrate comprising a first semiconductor material and having a top surface, and defining an opening having a non-crystalline sidewall proximate the top surface of the crystalline semiconductor substrate. An epitaxial film is formed in the opening. The epitaxial film includes a second semiconductor material that is lattice mismatched to the first semiconductor material. The epitaxial film has a growth front, the growth front including a surface having a facet not parallel to the substrate top surface. A dislocation in the epitaxial film is approximately normal to the epitaxial film surface.

Embodiments may include one or more of the following features. The non-crystalline sidewall may include a dielectric sidewall and/or have a sloped profile. The opening may be defined in a dielectric material disposed over the top surface of the substrate. The facet may define an angle α with the top surface of the substrate, and an aspect ratio H of a height h of the opening to a width w of the opening is greater than or equal to (tan α+1/tan α)/2. The height h may be selected from the range of 0.05 micrometer (μm) to 5 μm.

The opening may include a trench. In some embodiments, the dislocation in the epitaxial film is no more than about 8° off normal to the epitaxial film surface. The first semiconductor material may include a group IV element or compound, such as germanium and/or silicon, e.g., (100) silicon. The second semiconductor material may include at least one of a group IV element or compound, a III-V compound, or a II-VI compound. Examples of III-V compounds include aluminum phosphide (AlP), gallium phosphide (GaP), indium phosphide (InP), aluminum arsenide (AlAs), gallium arsenide (GaAs), indium arsenide (InAs), aluminum antimonide (AlSb), gallium antimonide (GaSb), indium antimonide (InSb), aluminum nitride (AlN), gallium nitride (GaN), indium nitride (InN), and their ternary and quaternary compounds. Examples of II-VI compounds includes zinc selenide (ZnSe), zinc telluride (ZnTe), cadmium selenide (CdSe), cadmium telluride (CdTe), zinc sulfide (ZnS), and their ternary and quaternary compounds.

In another aspect, the invention features a structure including a substrate comprising a first semiconductor material. An insulator layer is disposed over the substrate and defines a trench having a sidewall. A second semiconductor material is disposed in the trench, with the second semiconductor material being lattice mismatched to the first semiconductor material. A bottom portion of the second semiconductor material includes lattice defects, the defects are normal to the top surface of the second semiconductor material, and a profile of the top surface of the second semiconductor material is configured to direct the defects towards the sidewall.

In yet another aspect, the invention features a method for forming a structure, the method including defining an opening in a dielectric material disposed over a crystalline semiconductor substrate comprising a first semiconductor material. An epitaxial film is formed in the opening, the epitaxial film including a second semiconductor material lattice-mismatched to the first semiconductor material, the epitaxial film including a growth front having a surface, a dislocation in the epitaxial film being directed in a direction generally perpendicular to the growth front surface. The growth front surface defines an angle α with a top surface of the substrate such that the epitaxial film growth front surface is substantially non-parallel to a top surface of the substrate, and an aspect ratio H of a height h of the opening to a width w of the opening is greater than or equal to (tan α+1/tan α)/2.

In some embodiments, the opening defines a trench having a length at least twice the width w. The length of the trench may be at least 6 millimeters (mm), the width of the trench may be less than 400 nm, and/or the depth of the trench may be less than 490 nm. The substrate may be off-cut by up to about 6°. The second semiconductor material may include a first layer grown at a first set of processing conditions, and a second layer disposed over the first layer and grown at a second set of processing conditions. For example, the first layer may be grown at a first temperature and the second layer may be grown over the first layer at a second temperature, with the second temperature being higher than the first temperature. The first semiconductor material may include a group IV material and the second semiconductor material may include a III-V compound that possibly includes a cubic structure. A transistor or an opto-electronic device comprising at least a portion of the second semiconductor material may be formed.

In another aspect, the invention features a method for forming a structure, the method including defining a trench having a longitudinal axis and a dielectric sidewall disposed adjacent a substrate comprising a first semiconductor material. A second semiconductor material is epitaxially grown in the trench, the second semiconductor material having a lattice mismatch with the first semiconductor material. Defects arising from the lattice mismatch between the first and second semiconductor materials propagate away from the longitudinal axis of the trench in a direction substantially perpendicular to a growth front of the second material and are trapped by a sidewall of the trench.

One or more of the following features may be included. The length of the trench may be at least 6 mm, the width of the trench may be less than 400 nm, and/or the depth of the trench may be less than 490 nm. In some embodiments, the trench includes a first face and a second face, the longitudinal axis intersecting the first and second faces, and substantially no defects intersecting the first and second faces. The substrate may be off-cut by 6°. The second semiconductor material may include a buffer layer grown at a low temperature, and a growth layer may be disposed over the buffer layer and grown at a higher temperature. A transistor or an opto-electronic device comprising at least a portion of the second semiconductor material may be formed. Defining the trench may include plasma ashing.

In another aspect, the invention features a method for forming a structure, including defining a trench in a dielectric material disposed over a substrate comprising a first semiconductor material. The trench has a longitudinal axis and is filled with a second semiconductor material by growing a first layer at a first set of processing conditions and by growing a second layer over the first layer at a second set of processing conditions. Defects in the second semiconductor material are propagated away from the longitudinal axis and are trapped by a sidewall of the trench.

One or more of the following features may be included. The first semiconductor material may include a group IV material and the second semiconductor material may include a III-V compound. The III-V compound may include a cubic structure. The first layer may be grown at a first temperature and the second layer is grown over the first layer at a second temperature, the second temperature being higher than the first temperature.

In yet another aspect, the invention includes a method for forming a structure, the method including the steps of performing a selective etch to expose a crystal plane of a crystalline substrate including a first semiconductor material, and forming a dielectric layer over the substrate. An opening is defined in the dielectric layer to reveal the exposed crystal plane. A second semiconductor material is formed in the opening, and dislocations lying in a plane approximately normal to a growth surface of the second semiconductor material are directed to a sidewall of the opening.

In an aspect, the invention includes a method for forming a structure, the method including defining an opening in a dielectric material disposed over a crystalline semiconductor substrate comprising a first semiconductor material. An epitaxial film is formed in the opening, the epitaxial film including a second semiconductor material lattice-mismatched to the first semiconductor material. A growth front of the epitaxial film includes a surface. A dislocation in the epitaxial film is approximately normal to the epitaxial film surface, the epitaxial film surface defines an angle α with a top surface of the substrate, and the angle α is selected to direct the dislocation.

One or more of the following features may be included. The epitaxial film surface may include a facet that defines the angle α with respect to the top surface of the substrate, and an aspect ratio H of a height h of the opening to a width w of the opening is greater than or equal to (tan α+1/tan α)/2. The aspect ratio H may be greater than 0.5. The height h may be selected from the range of 0.05 μm to 5 μm. The angle α may be between about 0° and 90°.

In another aspect, the invention features a method for forming a structure, the method including defining an opening in a dielectric material disposed over a crystalline semiconductor substrate comprising a first semiconductor material. An epitaxial film is formed in the opening, the epitaxial film including a second semiconductor material lattice-mismatched to the first semiconductor material. The epitaxial film also includes a growth front that includes a surface, a dislocation in the epitaxial film being directed in a direction substantially perpendicular to the surface. The surface defines an angle α with a top surface of the substrate, and an aspect ratio H of a height h of the opening to a width w of the opening is greater than or equal to (tan α+1/tan α)/2.

One or more of the following features may be included. A dislocation in the epitaxial film may be directed in a direction within about 8° of a line perpendicular to the surface of the growth front. The angle α is typically selected such that the epitaxial film surface directs the dislocation to a sidewall of the opening. The epitaxial film surface may include a facet that defines an angle α with the top surface of the substrate. The aspect ratio H may be greater than 0.5. The height h may be selected from the range of 0.05 μm to 5 μm. The angle α may be selected from the range of between about 0° and 90°.

In another aspect, the invention includes a method for forming a structure, the method including defining an opening in a dielectric material disposed over a crystalline semiconductor substrate comprising a first semiconductor material. An epitaxial film is formed in the opening, the epitaxial film including a second semiconductor material that includes a growth front that includes a facet. The facet is selected such that a plane normal to the facet defines an angle θ with a sidewall of the opening and the facet directs the dislocation to the sidewall in a direction generally normal to the facet. The angle θ may between about 0° and 90°.

In another aspect, the invention includes a method for forming a structure, including defining a trench in a dielectric material disposed over a substrate comprising a first semiconductor material. The trench is filled with a second semiconductor material having a lattice mismatch with the first semiconductor material. Defects arising from the lattice mismatch between the first and second semiconductor materials propagate in a direction substantially perpendicular to a growth front of the second material and are trapped by a sidewall of the trench, with the trench having an arbitrary length.

BRIEF DESCRIPTION OF FIGURES

FIG. 1 is a schematic diagram illustrating defect trapping for the case of “slip dislocations” as defined below;

FIG. 2 is a schematic diagram showing the crystallography of mismatch relaxation related glissile threading dislocations and their projections onto (110) plane (w is the width of the opening while h is the height of the sidewall);

FIG. 3 is a schematic diagram illustrating redirection of dislocations in accordance with an aspect of the invention;

FIGS. 4a and 4b are graphs illustrating the effect of growth rate ratios on facet formation;

FIGS. 5a and 5b are schematic diagrams illustrating defect trapping;

FIG. 6 is an illustration of a simple model for aspect ratio trapping of growth dislocations;

FIG. 7 is a graphical representation illustrating a preferred aspect ratio for a given angle α between a facet and a top surface of the substrate, under the simplifying assumptions of r₁>>r₂, where r₁ and r₂ are the growth rates of (1) the epitaxial surface parallel to the underlying substrate and (2) the growth rate of the faceted epitaxial surface, respectively;

FIGS. 8a-8b are schematic diagrams illustrating facet dependence upon dielectric sidewall material;

FIGS. 9a-9b are schematic diagrams illustrating facet dependence upon dielectric sidewall profile;

FIG. 10a-10b is a schematic diagram of a structure designed to promote steep facets and more effective ART;

FIGS. 11a-11b are schematic diagrams-illustrating facet dependence upon dielectric sidewall orientation;

FIGS. 12a-12b are schematic diagrams-illustrating facet dependence upon epitaxial doping type;

FIG. 13 is a schematic diagram illustrating defect redirection toward a dielectric sidewall for the case of a curved and non-faceted surface; and

FIGS. 14a-14d are schematic cross-sectional views illustrating a structure including faceted openings defined in a substrate, formed in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

Referring to FIG. 1, a substrate 100, e.g., a crystalline semiconductor substrate, includes a first semiconductor material. The substrate 100 may be, for example, a bulk silicon wafer, a bulk germanium wafer, a semiconductor-on-insulator (SOI) substrate, or a strained semiconductor-on-insulator (SSOI) substrate. The substrate 100 may include or consist essentially of a first semiconductor material, such as a group IV element, e.g., Ge or Si. In an embodiment, substrate 100 includes or consists essentially of (100) silicon.

A non-crystalline material, such as a dielectric layer 110, is formed over the semiconductor substrate 100. The dielectric layer 110 may include a dielectric material, such as silicon nitride or silicon dioxide. The dielectric layer 110 may be formed by a method known to one of skill in the art, e.g., thermal oxidation or plasma-enhanced chemical vapor deposition. As discussed below, the dielectric layer may have a thickness t₁ corresponding to a desired height of crystalline material to be deposited in an opening formed through the dielectric layer. In some embodiments, the thickness t, of the dielectric layer 110 may range from, e.g., 25 nm to 2000 nm.

A mask (not shown), such as a photoresist mask, is formed over the substrate 100 and the dielectric layer 110. The mask is patterned to expose at least a portion of the dielectric layer 110. The exposed portion of the dielectric layer 110 is removed by, e.g., reactive ion etching (RIE) to define an opening 120, which extends to a surface of the substrate 100 and may be defined by at least one sidewall 130, e.g., a non-crystalline sidewall. The height h of sidewall 130 may be at least equal to a predetermined vertical distance H from the surface of the substrate. For a semiconductor grown epitaxially in this opening, where the lattice constant of the semiconductor differs from that of the substrate, it is possible to trap crystalline defects in the epitaxial region at the epitaxial layer/sidewall interface, within the predetermined distance H, when the ratio of H to the width w of the opening is properly chosen. Criteria for selecting the appropriate H/w ratio are discussed below.

The opening 120 may be a trench, i.e., it may be substantially rectangular in terms of cross-sectional profile, a top view, or both, and have a width w that is smaller than a length l (not shown) of the opening. For example, the width w of the opening may be less than about 500 nm, e.g., about 10-100 nm, and the length l of the opening may exceed each of w and H. The height h of the opening may be selected from a range of 0.05 μm to 5 μm. A ratio of the height h of the opening to the width w of the opening 120 may be ≧0.5, and in some embodiments, ≧1. The length l may be at least twice the width w.

A second crystalline semiconductor material 140 is formed in the opening 120. The second crystalline semiconductor material 140 may include or consist essentially of a group IV element or compound, a III-V compound, or a II-VI compound. Examples of suitable group IV elements or compounds include Ge, silicon germanium (SiGe), and silicon carbide (SiC). Examples of suitable III-V compounds include GaAs, GaP, GaSb, GaN, InAs, InP, InSb, InN, AlAs, AlP, AlSb, AlN, and/or their ternary or quaternary compounds. Examples of suitable II-VI compounds include ZnSe, ZnTe, CdSe, CdTe, ZnS, and/or their ternary or quaternary compounds.

The second crystalline semiconductor material 140 may be formed by selective epitaxial growth in any suitable epitaxial deposition system, including, but not limited to, metal-organic chemical vapor deposition (MOCVD), atmospheric-pressure CVD (APCVD), low- (or reduced-) pressure CVD (LPCVD), ultra-high-vacuum CVD (UHVCVD), molecular beam epitaxy (MBE), or atomic layer deposition (ALD). In the CVD process, selective epitaxial growth typically includes introducing a source gas into the chamber. The source gas may include at least one precursor gas and a carrier gas, such as, for example, hydrogen. The reactor chamber may be heated by, for example, RF-heating. The growth temperature in the chamber may range from about 300° C. to about 1100° C., depending on the composition of the crystalline material and the desired growth rate. The growth system may also utilize low-energy plasma to enhance the layer growth kinetics.

The epitaxial growth system may be a single-wafer or multiple-wafer batch reactor. Suitable CVD systems commonly used for volume epitaxy in manufacturing applications include, for example, an Aixtron 2600 multi-wafer system available from Aixtron, based in Aachen, Germany; an EPI CENTURA single-wafer multi-chamber systems available from Applied Materials of Santa Clara, Calif.; or EPSILON single-wafer epitaxial reactors available from ASM International based in Bilthoven, The Netherlands.

Dislocation defects 150 in the second crystalline semiconductor material 140 reach and terminate at the sidewalls of the opening 120 in the dielectric layer 110 at or below the vertical predetermined distance H from the surface of the substrate, such that dislocations in the second crystalline semiconductor material 140 decrease in density with increasing distance from the bottom portion of the opening 120. Accordingly, the bottom portion of the second crystalline semiconductor material 140 comprises lattice defects, and the upper portion of the crystalline material is substantially exhausted of crystalline defects. Various crystalline defects such as threading dislocations, stacking faults, twin boundaries, or anti-phase boundaries may thus be substantially eliminated from the upper portion of the crystalline material.

One possible origin of the threading dislocations in Ge epitaxial layers grown on Si substrates is the glide and expansion of dislocation half-loops formed during the mismatch relaxation process. In general, dislocations of this type are referred to herein as “slip dislocations.” These are glissile dislocations that can glide in response to epitaxial layer strain. For a crystalline semiconductor with a cubic structure, such as Si, Ge, GaAs, InP, etc., a common dislocation of this type that occurs during mismatched epitaxy is the 60° dislocation (where 60° is the angle between the dislocation line and the dislocation Burgers vector) located on {111} glide planes. FIG. 1 illustrates trapping of such glissile threading dislocations, which are typically oriented along <110> crystalline directions. Thus, when the dislocation is directed toward a substantially vertical sidewall oriented in a <100> direction, as shown in FIG. 1, it will be trapped at a sidewall within a vertical distance from the substrate H=w*tan(45°), where 45° is the angle between the dislocation and the substrate. For other sidewall orientations, the requirement for H is slightly less straightforward; this may be understood from FIG. 2 as follows.

FIG. 2 shows directions in a cubic crystal 200, indicating the expected possible line directions of 60° threading dislocations (thick lines 210) and their projections onto the (110) plane (long dashed lines 220) where w and h indicate the height and width of the opening. Their projections onto the (110) plane form ˜55° angles with the [110] direction. Therefore, for an opening 120 with an aspect ratio larger than h/w=tan 55°, and with substantially vertical sidewalls oriented in a <110> direction, such glissile threads may be trapped solely due to their crystallographic geometry, i.e., solely due to their preferred orientation after experiencing glide.

However, in an embodiment with a Si (100) substrate, threading dislocations with line direction along approximately the [001] growth direction may be created during growth. These threading dislocations will not necessarily be trapped merely by appropriate choice of sidewall orientation and sidewall height. This behavior may be understood in view of the concept of “growth dislocations,” which are distinguished here from slip dislocations. Growth dislocations are connected with the growth front and proceed with it via replication during growth. The line direction of a growth dislocation is a function of its Burgers vector and the crystal growth direction, and is generally approximately normal (usually within ˜10°, e.g., no more than about 8° off normal) to the growth face, i.e., epitaxial film surface, that the dislocation intersects; growth dislocations are assumed not to experience significant glide. This behavior is distinct from that of slip dislocations, which experience significant glide during relaxation of mismatched strain.

Methods for trapping this type of threading dislocation are disclosed below. As shown in FIG. 3, a growth surface 300 (also referred to herein as a growth front) of an epitaxial film of the second crystalline semiconductor material 140 grown in the opening in dielectric material 110 may tend to form facets 310 before the sidewall is fully covered by the epitaxial film. “Facet” is used herein to denote any surface of the epitaxial material that is not parallel to an underlying substrate surface 315. Whether or not facets form, and what crystal planes the facets comprise if they do form, depends upon various parameters, e.g., material grown, epitaxial process conditions such as pressure and temperature, sidewall dielectric material, and sidewall dielectric profile. These epitaxial film-formation parameters may be configured to cause facet formation. Thus, a profile of a top surface of the second crystalline semiconductor material 140 (i.e., the growth surface 300) may be configured to direct defects towards the sidewall 130.

As mentioned above, during crystal growth, a growth dislocation 320 is typically oriented approximately normal, i.e., generally perpendicular, to the growth surface 300 that the dislocation intersects. The growth surface geometry may evolve during growth because of differences in growth rates along different crystallographic directions. A given growth surface may increase in area at the expense of an adjacent growth surface, as illustrated conceptually in FIGS. 4a and 4b . One may define two growth rates r₁ and r₂, where r₁ is the growth rate of the epitaxial surface parallel to the underlying substrate and r₂ is the growth rate of the faceted epitaxial surface. In FIG. 4a , the ratio r₁/r₂ is high, leading to a smaller value of h₁, whereas in FIG. 4b , the ratio r₁/r₂ is low, leading to a larger h₁, where h₁ is the distance from the opening bottom to the point at which the facets fully consume the central growth surface.

A growth dislocation will typically experience redirection when the orientation of the surface it intersects changes. In other words, since a growth dislocation is typically replicated in a direction normal to the growth surface during epitaxy, if the growth surface orientation changes, the growth dislocation direction will also change. In the absence of faceting, if the growth surface is parallel to the substrate surface, growth dislocations will typically be oriented approximately perpendicular to the substrate. This means that they may not be trapped by substantially vertical sidewalls, regardless of the opening's aspect ratio. When faceting is present, the facets are typically initiated at the beginning of epitaxial growth at the edges of the opening; they progressively “consume” more and more of the growth surface as shown in FIGS. 4a and 4b . This leads to redirection of growth dislocations away from the opening center and toward the opening sidewalls, leading to dislocation trapping. This behavior has been observed experimentally by using SiGe marker layers to indicate facet evolution during growth of Ge in an opening in SiO₂ on a Si (100) surface. Clearly, faceting can greatly increase the effectiveness of aspect ratio trapping.

More specifically, the following experimental conditions were used to engineer facets to effectively direct growth dislocation segments to the sidewalls. Starting with a Si (001) substrate having a 500 nm-thick thermal oxide overlayer patterned with vertical sidewall openings 200 nm wide and larger, oriented along the [110] direction, Ge layers were grown using a two-step process including growth of a low-temperature buffer layer at 400° C. and growth of a second layer at a higher temperature of 600° C. For the purpose of delineating facet evolution, SiGe marker layers of approximately 10%-15% Si content were periodically inserted. This step is not required for the ART technique, but was done merely for the purposes of elucidating the process. For analysis, cross-sectional and plan-view transmission electron microscopy (TEM) specimens were prepared by mechanical thinning followed by Ar ion-milling. TEM analysis was conducted on a JEOL JEM 2100 microscope.

The threading dislocations revealed in samples prepared under these experimental conditions cannot be “slip dislocations” as the term is used herein. The dominant slip dislocation expected to occur in this material system is the 60° threading dislocation discussed above, typically oriented along a <110> direction. The projection of such a dislocation onto the (110) TEM specimen plane would form a 55° angle with the substrate (as can be understood from FIG. 2), regardless of the growth surface orientation. Contrary to this expected behavior of a slip dislocation, the threading dislocation segments observed in these samples appear to approximately follow directions normal to the growth surface (within around 8°), and often have an angle relative to the substrate that is not substantially equal to 55°. Most significantly, if a threading dislocation segment subsequently encounters a growth surface of a different orientation, it undergoes significant redirection to follow the direction normal to this latter surface. Clearly these configurations are not the result of lattice mismatch-driven half-loop expansion.

A sample was thinned from the substrate side down to a thickness of ˜200 nm; both the Si substrate and the first ˜300 nm of the epitaxial layer (where the defect trapping occurred) were removed, leaving only a defect-free Ge layer. TEM analysis of the quality of the Ge layer showed the effectiveness of the ART technique and using facet growth to direct growth of dislocations so that they are trapped within the ART region.

Referring also to FIGS. 5a and 5b , further experiments demonstrated effective trapping of threading dislocations in trenches of arbitrary length. These experiments began with substrate 100 including a first semiconductor material, i.e., 200 mm diameter p-type Si(001) substrates, 6° off-cut along the [110] direction and dielectric layer 110 disposed thereover, i.e., a 500 nm-thick thermal oxide. The dielectric material was patterned to define openings 120 configured as trenches along the [1 10] direction having 0.2-2.5 μm width using conventional photolithography and RIE. The trenches include a longitudinal axis 500. The trenches also include first and second faces 510, 520, with the longitudinal axis intersecting the first and second faces 510, 520.

RIE with CF_(x) chemistries can leave a fluorocarbon residue on the surface, causing defective epitaxial layers in subsequent growth. To remove this residue in preparation for epitaxial growth, an oxygen plasma ashing step (800 W at 1.2 Torr for 30 minutes) was carried out after RIE. The patterned substrates were then cleaned in Piranha, SC2, and dilute HF solutions sequentially. The final trench height (i.e., depth) was 490 nm after this cleaning procedure.

The trenches were filled with second crystalline semiconductor material 140 having a lattice mismatch with the first semiconductor material. In particular, the second crystalline semiconductor material was deposited in 450 nm-thick Ge layers, comprising a first layer 141 (e.g., a low-temperature buffer layer) and a second layer 142 (e.g., a higher-temperature growth layer), which were grown at 400 and 600° C., respectively, using an ASM Epsilon E2000 commercial-grade epitaxy reactor. Cross-sectional and plan-view TEM samples were prepared by mechanical polishing and Ar ion milling. TEM images were taken on a JEOL JEM 2100 microscope operating at 200 kV. Cross-sectional TEM images of Ge layers in trenches of 200 nm width and 400 nm width were prepared. These structures have ARs of 2.45 and 1.23, respectively. In the first sample, it was seen that the dislocations originating at the Ge/Si interface terminate at the oxide sidewall 130 below 200 nm and that complete trapping occurred within the first 200 nm of Ge growth. Furthermore, there was no evidence of either defect generation along the SiO₂ sidewall or of interactions within the trench causing defects to deflect and zigzag out of the trench. Defects, e.g., threading dislocations 150 arising from the lattice mismatch between the first and second semiconductor materials, propagated away from a longitudinal axis 500 of the trench in a direction substantially perpendicular to a growth front of the second material and were trapped by a sidewall of the trench. As a result, a completely defect-free region was created as the growth proceeded beyond the defect-trapping region. Moreover, substantially no defects intersect the first and second faces 510, 520. Here, a defect-free region of about 300 nm in thickness was demonstrated. Similarly, for the 400 nm-width structure, the defect-trapping region was about 400 nm thick. The final thickness of the defect-free region was about 100 nm. A trench suitable for fabrication in accordance with embodiments of the invention may have a length l of at least 6 mm, a width of less than 400 nm and/or a depth of less than 490 nm.

The mechanism of ART was further illustrated with plan-view TEM images of Ge layers in trenches of 360 nm width and 700 nm width. The AR was 1.36 and 0.7, respectively. Here the TEM captured the entire thickness of the Ge-filled trenches. It was found that the dislocations in Ge area terminate at the oxide sidewall. For AR>1, most of the dislocations were trapped by the oxide sidewall, which is not the case with AR<1. For this latter case many dislocations terminate at the SiO₂ sidewall, but some terminate instead at the Ge surface.

Trapping for AR>1 has previously been predicted based on the preferred defect geometry in the <110>{111} diamond cubic slip system. For growth on an (001) surface of substrate 100, misfit segments lie at the heteroepitaxial interface along <110> directions, with the threading segment rising up on (111) planes in <011> directions, making a 45° angle to the underlying Si (001) substrate 100 as shown in FIG. 5. Thus, for AR>1 threading dislocations will be trapped by a (100)-oriented sidewall of the epitaxial material, leading to a defect-free top epitaxial layer on Si.

In order to definitively demonstrate regions of defect-free Ge by ART, the TEM sample used for generation of plan views of Ge layer in trenches of 360 nm width and 700 nm width was thinned further, removing the dislocation-trapping region and imaging the overlying defect-free region. As is typical with a plan-view TEM sample preparation technique, a wedge-shaped sample was created. Convergent beam diffraction patterns were used to measure the thickness at the center of the sample. This was found to be about 70 nm. For trenches with a width of 290 nm, multiple adjacent trenches were completely dislocation-free except for one defect in the thickest part of the sample where the sample begins to encroach on the underlying trapping region. This is consistent with the cross-section TEM results, assuming the thickness of the heavily dislocated region to be approximately equal to the width of the trench.

These results offer a compelling new path for adding new semiconducting materials to the Si CMOS technology platform. Only conventional tools and techniques, in common use in Si CMOS manufacturing, were used to fabricate these samples. Furthermore, the thermal budget was low enough such that the Ge (or other materials such as II-VI or III-V compounds) could be added at any time in a CMOS process. Given the growing interest in replacing Si in the CMOS channel with Ge (for PMOS) and eventually with III-V materials (for NMOS), it is worth noting that the feature size achieved (400 nm with full trapping) is already large enough to serve as the active area for leading-edge CMOS logic transistors, assuming, as an example, a single planarized ART region per transistor.

In summary, regions of Ge up to 400 nm wide and free of near-surface defects were demonstrated via ART in SiO₂ trenches on Si using conventional photolithography and selective growth of Ge layers as thin as 450 nm. All of the dislocations originating at the Ge/Si interface were trapped at the oxide sidewall without the additional formation of defects at the sidewall for trenches having AR>1. By removing the dislocation-trapping region in plan-view TEM sample preparation, it is possible to obtain defect-free Ge. This approach utilized standard commercial equipment for all parts of the fabrication process and demonstrates a commercially viable way to integrate Ge and III-V materials as well with Si CMOS technology. Transistors and/or opto-electronic devices may be formed, which in some embodiments include at least a portion of the second semiconductor material formed in trenches defined in dielectric materials.

Growth dislocations may either be created at the substrate/epitaxial layer interface (for example, to accommodate local nonuniformity or disregistry) or by replication of pre-existing threading dislocations that intersect the growth front. These pre-existing threading dislocations may, for example, be segments of glissile dislocation loops that glide from the growth surface to the substrate/epitaxial layer interface under the influence of lattice-mismatch stress during the earlier stages of growth. Thus, it is possible for a single dislocation line to have both a slip dislocation segment and a growth dislocation segment.

Based on the observed behavior, it is possible to calculate the critical aspect ratio for growth-dislocation trapping under certain simplifying assumptions. FIG. 6 depicts a model for the case of a single type of non-{100} facet nucleating immediately upon initiation of growth at the pattern edges, and assuming dislocation 320 orientation perfectly normal to the local growth surfaces 300. Here, w is the width of the opening, and α is the angle between the substrate surface 315 and the dominant growth facet 310. The non-{100} facets grow and eventually consume the (001) central surface as discussed with respect to FIGS. 4a and 4b , assuming growth rate r₁ of the (001) surface is higher than growth rate r₂ of the non-{100} facet. h₁ is the distance from the opening bottom to the point at which the non-{100} facet fully consume the (001) growth surface; h₂ is the height that it takes for a dislocation 320 bent at the critical point C to be trapped by the sidewall. h₁ is determined by α and the ratio of the growth rate of the non-{100} facet to that of the (001) surface, r₂/r₁; h₂ depends only on a. The expressions for these are:

$\begin{matrix} {{h_{1} = {\left( \frac{w}{2} \right)\left( \frac{\tan\mspace{14mu}\alpha}{1 - \frac{r_{2}}{r_{1}\mspace{11mu}\cos\mspace{11mu}\alpha}} \right)}},} & \left( {{Eq}.\mspace{14mu} 1} \right) \\ {h_{2} = {\left( {w\mspace{11mu}\cot\mspace{11mu}\alpha} \right)\text{/}2.}} & \left( {{Eq}.\mspace{14mu} 2} \right) \end{matrix}$ Note that for the case of r₁>>r₂, a situation that was approximated in experiments as evidenced by the far greater spacing between marker layers in the (001) direction, this simplifies to h₁=(w tan α)/2. Two dislocations ACD and BCD are used to illustrate the model. For dislocation ACD, segment AC is of glissile nature and is created during the relaxation of mismatch stress, early in the epitaxial growth process. During subsequent growth, instead of simply continuing in its original orientation, it is redirected in the direction normal to the growth surface it encounters, i.e. the non-{100} facet. The aspect ratio required for trapping of ACD is (h₁+h₂)/w. Dislocation BCD is an example of the redirection and trapping of an existing growth dislocation below point C (segment BC is of growth nature and oriented approximately along the [001] growth direction). Again, the aspect ratio for successful trapping is (h₁+h₂)/w. For either case, the existing threading dislocations below point C may be deflected from the middle to either side (depending on the exact location of the original dislocation) regardless of their original directions and nature.

To summarize, an important factor influencing the direction of threading dislocations toward the dielectric sidewalls in ART, for the case of facets forming early in the growth process, is the influence of growth facets causing threading dislocations to replicate approximately along the local facet normal, hence directing them to the sidewalls. However, it should be noted that, if mismatch generates glissile threading segments (i.e., “slip dislocations”) in the later stages of growth, these segments are not likely to have the opportunity to be converted to growth dislocations; therefore, the preferred crystallographic geometry of such slip dislocations, as discussed previously, will play the dominant role in their trapping.

Structures may be designed to encourage faceting to increase the efficacy of dislocation trapping and reduce the required height of opening sidewalls. Formation of facets that have a high inclined angle with respect to the sidewall at an early stage of growth is highly desired. This can clearly be understood from the simple model that applies for the case of r₁>>r₂ as discussed above, where the preferred aspect ratio for growth dislocation trapping is (h₁+h₂)/w=(tan α+cot α)/2. For a given w, this aspect ratio is minimized for α=45°. FIG. 7 depicts graphically the aspect ratio preferred for trapping growth dislocations based on redirection via faceting, as predicted by this simple model for the case of r₁>>r₂.

Epitaxial film-formation parameters may be configured to cause the formation of a facet, i.e., to enhance facet formation. Examples of film-formation parameters that may be configured include:

(1) Selection of a sidewall dielectric material so that the system has a high interface free energy between the dielectric material and the second crystalline semiconductor material to be deposited in the opening;

(2) Design of the geometry of the dielectric sidewall;

(3) Engineering of the epitaxial growth conditions, for example, growth temperature;

(4) Choosing the orientation of the dielectric sidewall relative to a given crystallographic direction; and

(5) Choosing the doping condition of the epitaxially deposited semiconductor material.

As shown in FIGS. 8a-8b , the dielectric material of the dielectric layer 110 in which the opening 120 is defined may be selected to enhance facet formation and defect trapping. For example, by employing a dielectric material with a relatively high interface free energy between the dielectric material and the epitaxial material to be grown in the opening, i.e., the second crystalline semiconductor material, facets 800 with a high inclination angle with respect to the sidewall may be introduced and hence improve the trapping efficacy of dislocations. For example, referring to FIG. 8a , silicon nitride may be used as a dielectric layer 110 to encourage formation of steep facets 800. An exemplary process includes deposition of a silicon nitride layer, with a preferred thickness ranging from 20 nm to 5 μm, on a substrate, e.g., a (100) Si substrate. The silicon nitride layer may be deposited at 780° C. by any LPCVD technique. A photoresist layer is formed to define openings, and the silicon nitride material in these openings is removed, for example by means of an RIE that stops selectively on the Si surface. Then a selective epitaxial layer of a second crystalline semiconductor material, such as Ge, at a temperature of 585° C., is deposited in these openings by, for example, MOCVD. The epitaxial material deposited in this structure with silicon nitride sidewalls 130 is expected to form (111) facets on the edges next to the sidewalls 130.

In comparison, using silicon dioxide as the dielectric material 110 for the sidewalls, as shown in FIG. 8b , can result in a lower inclination angle of the facets 800 in comparison to silicon nitride material 110 for the sidewalls 130.

Experimental results demonstrated different faceting behavior between the selective epitaxial layer of Si grown on Si substrate in a silicon nitride opening and that grown in a silicon oxide opening. The selective Si epitaxial layer tends to form {311} facets adjacent to silicon oxide sidewalls, while it tends to form {111} facets adjacent to silicon nitride sidewalls. In this example, a {111} facet has a higher inclined angle with respect to the sidewall than does a {311} facet. Although this experiment was performed with Si epitaxial growth, similar behavior can be expected for selective epitaxial growth of other materials, such as Ge and III-V materials.

In another embodiment, with reference to FIG. 9a-9b , the geometry of the dielectric sidewall 130 that bounds the opening 120 is selected to encourage the formation of facets 800. More specifically, a gradually sloped dielectric sidewall is more likely to encourage steeply inclined facet formation than a substantially vertical dielectric sidewall. FIG. 9a shows such a dielectric sidewall 130 with a gradually sloped profile. In contrast to the dielectric with vertical sidewall as shown in FIG. 9b , such a gradually sloped profile tends to encourage the formation of steep facets 800. Gradually sloped sidewalls can be obtained in a variety of ways, including, for example, sidewalls with a slope of about 25 to 40 degrees off vertical by wet etching or sidewalls with a slope of about 6 to 12 degrees off vertical by dry etching.

The strong dependence of faceting of a lattice-matched material on sidewall profile has been demonstrated in the literature. For example, R. Loo, et al., J. Elec. Soc. 150 (10), G638 (2003) show two samples of lattice-matched Si epitaxial layers selectively grown on a Si substrates in openings bounded by silicon nitride dielectric sidewalls. Experimental results indicate that the deposited epitaxial layer tends to form {111} facets at a gradually sloped sidewall and {311} facets at a vertical sidewall. Since the {111} facet has a higher inclined angle with respect to the substrate surface than does the {311} facet, the case of a sloped dielectric sidewall geometry can be a preferred condition for dislocation trapping. Embodiments of the present invention include selective epitaxial growth of lattice-mismatched materials, such as Ge and III-V materials on Si substrates, with sidewall profiles engineered to cause formation of facets in the epitaxially grown material.

Without a substantially vertical sidewall, a greater height/width aspect ratio may be required to trap dislocations. To solve this conflicting design criterion for the sidewall profile, a dielectric sidewall 130 with a gradually sloped bottom portion and a substantially vertical top portion may be used, as illustrated in FIG. 10a . As described above, the gradually sloped bottom portion may introduce desirable, steeply inclined faceting at the early stage of the growth and enhance the dislocation trapping efficacy; the substantially vertical top portion is preferred for effectively trapping the defects that have been redirected. An alternative embodiment that is expected to have the same effect is shown in FIG. 10b , in which the bottom portion of the dielectric sidewall 130 defines a step.

Growth conditions for the lattice-mismatched epitaxial layer may be designed to encourage defect trapping by faceting. Epitaxial layer growth conditions, such as growth temperature, may significantly affect faceting. For example, a low epitaxial growth temperature, such as ˜450-550° C. for selective Ge epitaxial growth on Si substrate, may be chosen to encourage the epitaxial layer to form a steeper facet, i.e., a facet with higher inclination angle with respect to the sidewall. The strong dependence of faceting of lattice-matched materials on growth temperature has been demonstrated in the literature. For example, S. Lim, et al., J. Vac. Sci. Technol. B 22(2), 682 (2004), show several samples of a selective silicon epitaxial layer grown on a Si substrate in openings bound by silicon dioxide. Images taken from samples grown at temperatures of 550° C., 600° C. and 650° C. in sequence show that the growth conditions affect faceting. The (111) facet tends to form at the early growth stage at lower growth temperature, while the (211) facet forms at higher growth temperature. Again, since the angle between the (111) facet and the substrate is larger than that of the (211) facet, the dislocations are trapped more effectively in the former case. Embodiments of the present invention include selective epitaxial growth of lattice-mismatched materials, such as Ge and III-V materials on Si substrates, with facets being formed by the engineering of growth conditions such as growth temperature. Thus, dislocations may be trapped more effectively by desirable faceting.

Although a more steeply inclined facet is generally superior for growth dislocation trapping, in practice the steepest desirable inclination is about 45° in most circumstances. This is clear from the simplified model as described with respect to FIG. 7. For epitaxy of cubic semiconductors grown adjacent to dielectric sidewalls, facets steeper than 45° are not typically encountered.

Referring to FIGS. 11a-11b , the orientation of the dielectric sidewalls 130 bounding the opening may influence the faceting of the selectively grown epitaxial layer 140. Therefore, the geometric pattern of the dielectric layer 110 may be designed to enhance the desirable faceting and hence improve the efficacy of dislocation trapping. For example, for selectively grown lattice-mismatched epitaxial layers, such a Ge, on a substrate 100 (e.g., {100} Si), growth may be substantially facet-free when the dielectric sidewalls 130 are oriented in <100> directions (shown in FIG. 11a ). In comparison, epitaxial growth adjacent to dielectric sidewalls oriented in <110> directions will typically introduce facets (shown in FIG. 11b ). Therefore, a dielectric sidewall oriented in a <110> direction is expected to lead to greater efficiency in trapping growth dislocations than a dielectric sidewall oriented in a <100> direction.

In another embodiment, as illustrated in FIGS. 12a-12b , the doping of the selectively grown epitaxial material 140 may be engineered to enhance facets 800 with steeper inclination angles, thereby improving the defect trapping. For example, when an epitaxial layer is doped to improve the conductivity of the semiconductor material, the choice of dopants may affect the angle of facet inclination. A steep facet 800 may form during Si growth if a first dopant, e.g., boron is incorporated (FIG. 12a ), while a gradually sloped facet 800 may form if a second dopant, e.g., arsenic, is incorporated (FIG. 12b ). The steeper facet formed in the former case is more effective in dislocation trapping than the gradually sloped facet formed in the latter case. Varying doping conditions in the epitaxial layer leads to different facet geometry and inclination angle.

In another embodiment, with reference to FIG. 13, dislocations 150 may be guided even without the creation of facets. For the case of a curved growth surface, the growth dislocations will be guided to the sidewalls 130 in the case of convex curvature (i.e., thicker toward the middle of the opening, thinner at the edges), as illustrated in FIG. 13. A concave growth surface (thicker toward the edges and thinner at the middle) is preferably avoided, as this may guide dislocations to the center of the opening. A curved growth surface may occur under certain doping condition and sidewall orientations, for example, Si epitaxial material formed in openings bound by silicon dioxide sidewalls oriented in <100> directions, and in-situ doped with arsenic.

In yet another embodiment, facets defined in the substrate, prior to epitaxial growth, may be used to promote trapping of defects. As illustrated in FIG. 14a , a mask opening 1000 is defined in a photoresist layer 1010 formed over a top surface of substrate 100. A selective etch is performed to expose a specific crystal plane of the substrate in a bottom portion of the opening 1000. For example, a wet KOH etch may used to expose a (111) Si surface. The photoresist layer is subsequently removed.

Referring to FIG. 14b , dielectric layer 110 is defined over the substrate 100 (including a first semiconductor material as described above), and opening 120 is defined in the dielectric layer 110. The opening 120 may be defined by a selective removal process such as RIE, stopping at the top surface of the substrate 100 to reveal the exposed crystal plane. The opening sidewall defines an angle 0 with the substrate 100, with the angle 0 preferably being less than 90°.

Referring to FIG. 14c , second semiconductor material 140 is formed in the opening 120 by selective epitaxy. The initial epitaxial surface will form at approximately the same angle θ with the opening sidewall, such that dislocations lying in a plane approximately normal to the epitaxial surface will be redirected to the opening sidewall.

Referring to FIG. 14d , the opening 120 is filled with the second semiconductor material 140. Chemical-mechanical polishing (CMP) may be used to planarize a top surface of the epitaxial second semiconductor material. The low-defect epitaxial area may be used for subsequent device fabrication.

The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting on the invention described herein. Scope of the invention is thus indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are intended to be embraced therein. 

What is claimed is:
 1. A method comprising: defining an opening having a dielectric sidewall to a first crystalline semiconductor material of a substrate, the substrate having a top surface; and epitaxially growing a second crystalline semiconductor material in the opening, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, a dislocation in the second crystalline semiconductor material arising from the lattice mismatch, the epitaxially growing the second crystalline semiconductor material comprising inducing a facet in the second crystalline semiconductor material, the facet being non-parallel to the top surface of the substrate, the dislocation being directed to the dielectric sidewall in a direction within 10° of perpendicular to the facet.
 2. The method of claim 1 further comprising forming a dielectric layer over the top surface of the substrate, the opening being defined through the dielectric layer.
 3. The method of claim 1, wherein the dislocation intersects the dielectric sidewall in the direction.
 4. The method of claim 1, wherein the facet defines an angle α with the top surface of the substrate, an aspect ratio of a height of the opening to a width of the opening being greater than or equal to (tan α+cot α)/2.
 5. The method of claim 1, wherein the dielectric sidewall comprises at least a portion that is perpendicular to the top surface of the substrate.
 6. The method of claim 1, wherein the dielectric sidewall comprises at least a portion that is non-perpendicular to the top surface of the substrate.
 7. The method of claim 1, wherein the epitaxially growing the second crystalline semiconductor material comprises using epitaxial growth at a temperature equal to or less than 550° C.
 8. The method of claim 1, wherein the substrate is a {100} substrate, and the dielectric sidewall is oriented in a <110> direction.
 9. The method of claim 1, wherein the epitaxially growing the second crystalline semiconductor material comprises doping the second crystalline semiconductor material.
 10. A method comprising: forming a dielectric sidewall on a substrate, the substrate comprising a first crystalline semiconductor material and having a top surface; and epitaxially growing a second crystalline semiconductor material on the substrate and adjoining the dielectric sidewall, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, a dislocation in the second crystalline semiconductor material arising from the lattice mismatch, the epitaxially growing the second crystalline semiconductor material comprising forming a growth front of the second crystalline semiconductor material that is non-parallel to the top surface of the substrate, the dislocation being directed to the dielectric sidewall in a direction within 10° of perpendicular to the growth front, the dislocation terminating at the dielectric sidewall in the direction.
 11. The method of claim 10, wherein the growth front comprises a facet.
 12. The method of claim 10, wherein the growth front comprises a convex surface.
 13. The method of claim 10 further comprising forming a dielectric layer over the top surface of the substrate, an opening being defined through the dielectric layer, the dielectric sidewall being a sidewall of the opening.
 14. The method of claim 10, wherein the dielectric sidewall comprises at least a portion that is perpendicular to the top surface of the substrate.
 15. The method of claim 10, wherein the dielectric sidewall comprises at least a portion that is non-perpendicular to the top surface of the substrate.
 16. A method comprising: etching a first crystalline semiconductor material of a substrate to expose a crystallographic plane of the first crystalline semiconductor material that is non-parallel to a top surface of the substrate; defining a dielectric sidewall adjoining the crystallographic plane, the dielectric sidewall and the crystallographic plane defining a first angle less than 90°; and epitaxially growing a second crystalline semiconductor material from the crystallographic plane, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, a dislocation in the second crystalline semiconductor material arising from the lattice mismatch, the epitaxially growing the second crystalline semiconductor material comprising forming a growth front of the second crystalline semiconductor material, the growth front and the dielectric sidewall defining a second angle, the second angle being approximately equal to the first angle, the dislocation being directed to the dielectric sidewall in a direction within 10° of perpendicular to the growth front.
 17. The method of claim 16, wherein the crystallographic plane is a (111) surface.
 18. The method of claim 16, wherein the etching comprises using a KOH etch.
 19. The method of claim 16 further comprising: forming a first dielectric layer on the top surface of the substrate, the first dielectric layer having an opening exposing the top surface of the substrate, the etching the first crystalline semiconductor material being performed through the opening, and after the etching, the dielectric sidewall being defined in the opening.
 20. The method of claim 16, wherein a portion of the second crystalline semiconductor material distal from the crystallographic plane is substantially exhausted of dislocations. 